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Self-regulation of free charge carriers in perovskites via Schottky defect formation has been posited as the origin of the well-known defect tolerance of metal halide perovskite materials that are promising candidates for photovoltaic applications, like solar cells. Understanding the mechanisms of self-regulation, here for a representative of more commercially viable all-inorganic perovskites, promises to lead to the fabrication of better-performing solar cell materials with higher efficiencies. We investigated different mechanisms and pathways of the diffusion and recombination of interstitials and vacancies (Schottky pairs) in CsPbBr$_3$. We use Nudged Elastic Band calculations and ab initio-derived pseudopotentials within Quantum ESPRESSO to determine energies of formation, migration, and activation for these defects. Our calculations uncover defect pathways capable of producing an activation energy at or below the value of 0.53~eV observed for the slow, temperature-dependent recovery of light-induced conductivity in CsPbBr$_3$. Our work reveals the existence of a low-energy diffusion pathway involving a concerted "domino effect" interstitial mechanism, with the net result that interstitials can diffuse more readily over long distances than expected. Importantly, this observation suggests that defect self-healing can be promoted if the "domino effect" strategy can be engaged.

We used broadband local dielectric spectroscopy (BLDS), an electric force microscopy technique, to make non-contact measurements of conductivity in the dark and under illumination of PM6:Y6 and Y6 prepared on ITO and PEDOT:PSS/ITO. Over a range of illumination intensities, BLDS spectra were acquired and fit to an impedance model of the tip-sample interaction to obtain a sample resistance and capacitance. By comparing two descriptions of cantilever friction, an impedance model and a microscopic model, we connected the sample resistance inferred from impedance modeling to a microscopic sample conductivity. A charge recombination rate was estimated from plots of the conductivity versus light intensity and found to be sub-Langevin. The dark conductivity was orders of magnitude higher than expected from Fermi-level equilibration of the PM6:Y6 with the substrate, suggesting that dark carriers may be a source of open-circuit voltage loss in PM6:Y6.

We present an approach to the verification of systems for whose description some elements - constants or functions - are underspecified and can be regarded as parameters, and, in particular, describe a method for automatically generating constraints on such parameters under which certain safety conditions are guaranteed to hold. We present an implementation and illustrate its use on several examples., Comment: 26 pages. arXiv admin note: text overlap with arXiv:1910.05208

Simulation has become an essential component of designing and developing scientific experiments. The conventional procedural approach to coding simulations of complex experiments is often error-prone, hard to interpret, and inflexible, making it hard to incorporate changes such as algorithm updates, experimental protocol modifications, and looping over experimental parameters. We present mmodel, a framework designed to accelerate the writing of experimental simulation packages. mmodel uses a graph-theory approach to represent the experiment steps and can rewrite its own code to implement modifications, such as adding a loop to vary simulation parameters systematically. The framework aims to avoid duplication of effort, increase code readability and testability, and decrease development time.

The Unruh-DeWitt particle detector model has found success in demonstrating quantum information channels with non-zero channel capacity between qubits and quantum fields. These detector models provide the necessary framework for experimentally realizable Unruh-DeWitt Quantum Computers with near-perfect channel capacity. We propose spin qubits with gate-controlled coupling to Luttinger liquids as a laboratory setting for Unruh-DeWitt detectors and general design constraints that underpin their feasibility in this and other settings. We also present several experimental scenarios including graphene ribbons, edges states in the quantum spin Hall phase of HgTe quantum wells, and the recently discovered quantum anomalous Hall phase in transition metal dichalcogenides. Theoretically, through bosonization, we show that Unruh-DeWitt detectors can carry out Quantum Computations and when they can make perfect quantum communication channels between qubits via the Luttinger liquid. Our results point the way toward an all-to-all connected solid state quantum computer and the experimental study of quantum information in quantum fields via condensed matter physics., Comment: 12 pages, 7 figures, 1 table, version 3

In this paper, we study properties of certain risk measures associated with acceptance sets. These sets describe regulatory preconditions that have to be fulfilled by financial institutions to pass a given acceptance test. If the financial position of an institution is not acceptable, the decision maker has to raise new capital and invest it into a basket of so called eligible assets to change the current position such that the resulting one corresponds with an element of the acceptance set. Risk measures have been widely studied. The risk measure that is considered here determines the minimal costs of making a financial position acceptable. In the literature, monetary risk measures are often defined as translation invariant functions and, thus, there is an equivalent formulation as Gerstewitz-Functional. The Gerstewitz-Functional is an useful tool for separation and scalarization in multiobjective optimization in the non-convex case. In our paper, we study properties of the sublevel sets, strict sublevel sets and level lines of a risk measure defined on a linear space. Furthermore, we discuss the finiteness of the risk measure and relax the closedness assumptions., Comment: 35 pages

We analyze possibilities of second-order quantifier elimination for formulae containing parameters -- constants or functions. For this, we use a constraint resolution calculus obtained from specializing the hierarchical superposition calculus. If saturation terminates, we analyze possibilities of obtaining weakest constraints on parameters which guarantee satisfiability. If the saturation does not terminate, we identify situations in which finite representations of infinite saturated sets exist. We identify situations in which entailment between formulae expressed using second-order quantification can be effectively checked. We illustrate the ideas on a series of examples from wireless network research., Comment: 44 pages

Electric force microscopy was used to record the light-dependent impedance spectrum and the probe transient photoconductivity of a film of butylammonium lead iodide, BA$_{2}$PbI$_{4}$, a 2D Ruddlesden--Popper perovskite semiconductor. The impedance spectrum of BA$_{2}$PbI$_{4}$ showed modest changes as the illumination intensity was varied up to 1400 mW/cm$^{2}$, in contrast with the comparatively dramatic changes seen for 3D lead-halide perovskites under similar conditions. BA$_{2}$PbI$_{4}$'s light-induced conductivity had a rise time and decay time of $\sim$ 100 $\mu$s, 10$^{4}$ slower than expected from direct electron-hole recombination and yet 10$^{5}$ faster than the conductivity-recovery times recently observed in 3D lead-halide perovskites and attributed to the relaxation of photogenerated vacancies. What sample properties are probed by electric force microscope measurements remains an open question. A Lagrangian-mechanics treatment of the electric force microscope experiment was recently introduced by Dwyer, Harrell, and Marohn which enabled the calculation of steady-state electric force microscope signals in terms of a complex sample impedance. Here this impedance treatment of the tip-sample interaction is extended, through the introduction of a time-dependent transfer function, to include time-resolved electrical scanned probe measurements. It is shown that the signal in a phase-kick electric force microscope experiment, and therefore also the signal in a time-resolved electrostatic force microscope experiment, can be written explicitly in terms of the sample's time-dependent resistance (i.e., conductivity).

Films of (FA$_{0.79}$MA$_{0.16}$Cs$_{0.05}$)$_{0.97}$Pb(I$_{0.84}$Br$_{0.16}$)$_{2.97}$ were grown over TiO$_{2}$, SnO$_{2}$, ITO, and NiO. Film conductivity was interrogated by measuring the in-phase and out-of-phase forces acting between the film and a charged microcantilever. We followed the films' conductivity vs. time, frequency, light intensity, and temperature (233 to 312 K). Perovskite conductivity was high and light-independent over ITO and NiO. Over TiO$_{2}$ and SnO$_{2}$, the conductivity was low in the dark, increased with light intensity, and persisted for 10's of seconds after the light was removed. At elevated temperature over TiO$_{2}$, the rate of conductivity recovery in the dark showed an activated temperature dependence (E$_{a}$ = 0.58 eV). Surprisingly, the light-induced conductivity over TiO$_{2}$ and SnO$_{2}$ relaxed essentially instantaneously at low temperature. We use a transmission-line model for mixed ionic-electronic conductors to show that the measurements presented are sensitive to the sum of electronic and ionic conductivities. We rationalize the seemingly incongruous observations using the idea that holes, introduced either by equilibration with the substrate or via optical irradiation, create iodide vacancies.

Scanning probe microscopy is often extended beyond topographic imaging to study electrical forces and sample properties, with the most widely used experiment being frequency-modulated Kelvin probe force microscopy. The equations commonly used to interpret this experiment, however, rely on two hidden assumptions: (1) the tip charge oscillates in phase with the cantilever motion to keep the tip voltage constant, and (2) any changes in the tip-sample interaction happen slowly. Starting from an electro-mechanical model of the cantilever-sample interaction, we use Lagrangian mechanics to derive coupled equations of motion for the cantilever position and charge. This general approach rigorously describes scanned probe experiments even in the case when the usual assumptions of fast tip charging and slowly changing samples properties are violated. We develop a Magnus-expansion approximation to illustrate how abrupt changes in the tip-sample interaction cause abrupt changes in the cantilever amplitude and phase. We show that feedback-free time-resolved electric force microscopy cannot uniquely determine sub-cycle photocapacitance dynamics. We then use first-order perturbation theory to relate cantilever frequency shift and dissipation to the sample impedance even when the tip charge oscillates out of phase with the cantilever motion. Analogous to the treatment of impedance spectroscopy in electrochemistry, we apply this approximation to determine the cantilever frequency shift and dissipation for an arbitrary sample impedance in (broadband) local dielectric spectroscopy experiments. The general approaches we develop provide a path forward for rigorously modeling the coupled motion of the cantilever position and charge in the wide range of electrical scanned probe microscopy experiments where the hidden assumptions of the conventional equations are violated or inapplicable., Comment: 30 pages, 19 figures

Individual electron spins have been observed using magnetic resonance in combination with a number of distinct detection approaches. The coordinates of an individual electron spin can then in principle be determined by introducing a 10 to 100 nm diameter magnetic needle, scanning the needle, and collecting signal as a function of the needle's position. Although individual electrons have recently been localized with nanometer precision in this way using a nitrogen-vacancy center in diamond as the spin detector, the experiment's low signal-to-noise ratio limited acquisition to two-dimensional scanning of just a few dozen data points and was incompatible with nitroxide spin labels widely used to label proteins and nucleic acids. We introduce and numerically simulate a protocol for detecting and imaging individual nitroxide electron spins mechanically with high spatial resolution. In our protocol a scanned magnet-tipped cantilever is brought near the sample, modulated microwaves are applied to resonantly excite electron spins, and changes in spin magnetization are detected as a shift in the mechanical frequency of the cantilever. By carefully applying resonant microwaves in short bursts in synchrony with the cantilever's oscillation, we propose to retain high spatial resolution even at large cantilever amplitude where sensitivity is highest. Numerical simulations reveal nanometer-diameter rings of frequency-shift signal as the tip is scanned. Our primary finding is that it is possible --- using a Bayesian, reverse Monte Carlo algorithm introduced here --- to obtain the full three-dimensional distribution of electron coordinates from the signal rings revealed in a two-dimensional frequency-shift map. This reduction in dimensionality brings within reach, on a practical timescale, the angstrom-resolution three-dimensional imaging of spin-labeled macromolecules., Comment: 14 pages, 8 figures

High-quality spatially-resolved measurements of electric fields are critical to understanding charge injection, charge transport, and charge trapping in semiconducting materials. Here, we report a variation of frequency-modulated Kelvin probe force microscopy (FM-KPFM) that enables spatially-resolved measurements of the electric field. We measure electric field components along multiple directions simultaneously by employing position modulation and lock-in detection in addition to numeric differentiation of the surface potential. We demonstrate the technique by recording linescans of the in-plane electric field vector in the vicinity of a patch of trapped charge in a DPh-BTBT organic field-effect transistor. This technique is simple to implement and should be especially useful for studying electric fields in spatially inhomogeneous samples like organic transistors and photovoltaic blends., Comment: 5 pages, 4 figures, supplemental materials

Aligning a microcantilever to an area of interest on a sample is a critical step in many scanning probe microscopy experiments, particularly those carried out on devices and rare, precious samples. We report a series of protocols that rapidly and reproducibly align a high-compliance microcantilever to a $< 10 \: \mu\mathrm{m}$ sample feature under high vacuum and at cryogenic temperatures. The first set of protocols, applicable to a cantilever oscillating parallel to the sample surface, involve monitoring the cantilever resonance frequency while laterally scanning the tip to map the sample substrate through electrostatic interactions of the substrate with the cantilever. We demonstrate that when operating a cantilever a few micrometers from the sample surface, large shifts in the cantilever resonance frequency are present near the edges of a voltage-biased sample electrode. Surprisingly, these "edge-finder" frequency shifts are retained when the electrode is coated with a polymer film and a $\sim 10 \: \mathrm{nm}$ thick metallic ground plane. The second series of methods, applicable to any scanning probe microscopy experiment, integrate a single-optical fiber to image line scans of the sample surface. The microscope modifications required for these methods are straightforward to implement, provide reliable micrometer-scale positioning, and decrease the experimental setup time from days to hours in a vacuum, cryogenic magnetic resonance force microscope., Comment: 9 pages, 7 figures

We report achieving enhanced nuclear magnetization in a magnetic resonance force microscope experiment at 0.6 tesla and 4.2 kelvin using the dynamic nuclear polarization (DNP) effect. In our experiments a microwire coplanar waveguide delivered radiowaves to excite nuclear spins and microwaves to excite electron spins in a 250 nm thick nitroxide-doped polystyrene sample. Both electron and proton spin resonance were observed as a change in the mechanical resonance frequency of a nearby cantilever having a micron-scale nickel tip. NMR signal, not observable from Curie-law magnetization at 0.6 tesla, became observable when microwave irradiation was applied to saturate the electron spins. The resulting NMR signal's size, buildup time, dependence on microwave power, and dependence on irradiation frequency was consistent with a transfer of magnetization from electron spins to nuclear spins. Due to the presence of an inhomogenous magnetic field introduced by the cantilever's magnetic tip, the electron spins in the sample were saturated in a microwave-resonant slice 10's of nm thick. The spatial distribution of the nuclear polarization enhancement factor $\epsilon$ was mapped by varying the frequency of the applied radiowaves. The observed enhancement factor was zero for spins in the center of the resonant slice, was $\epsilon = +10$ to $+20$ for spins proximal to the magnet, and was $\epsilon = -10$ to $-20$ for spins distal to the magnet. We show that this bipolar nuclear magnetization profile is consistent with cross-effect DNP in a $\sim \! 10^{5} \: \mathrm{T} \: \mathrm{m}^{-1}$ magnetic field gradient. Potential challenges associated with generating and using DNP-enhanced nuclear magnetization in a nanometer-resolution magnetic resonance imaging experiment are elucidated and discussed., Comment: 20 pages, 9 figures, 4 supplementary figures, 58 references